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Q.

Two planets have the same average density but their radii are R₁ and R₂. If acceleration due to gravity on these planets be g₁ and g₂ respectively, then

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a

$\frac{g_{1}}{g_{2}} = \frac{R_{1}}{R_{2}}$

b

$\frac{g_{1}}{g_{2}} = \frac{R_{2}}{R_{1}}$

c

$\frac{g_{1}}{g_{2}} = \frac{R_{1}^{2}}{R_{2}^{2}}$

d

$\frac{g_{1}}{g_{2}} = \frac{R_{1}^{3}}{R_{2}^{3}}$

answer is A.

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Detailed Solution

$g = \frac{4}{3} πρGR$ . If $ρ$ = constant then $\frac{g_{1}}{g_{2}} = \frac{R_{1}}{R_{2}}$

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